Chapter 2 preliminary model results
Cameron Ho
2025-11-26
Modeling
I am using a conditional binomial model to determine what factors
impact movement decisions of territorial common ravens during the winter
in Yellowstone. I will look at if various predictors impact if a raven
decided to leaves its territory, and if it did, if it visit the Gardiner
hunting region or not. The largest predictors here revolve around food
availability of carrion created by human hunting activity and
wolves.
There are two data sets, one for each part of the conditional
model. The first one includes all of the days during the Yellowstone
Wolf Project winter study periods (Nov 15- Dec 15 & Mar 1 - Mar 30)
because my main predictor is the presence of wolf kills within a ravens
territory and the carcass data is most reliable for that period of time
due to GPS collar fix rates.
The second data set includes all winter from the start of the hunting
season (varies by year, but always in the last week of October) to the
end of March (end of late winter study). I can include these other
periods because I am no longer considering wolf kills as a predictor
because the raven at this point in the conditional model has already
decided to leave its territory. This also allows me to have more data on
days with low or no hunter gutpile availability from January and
February.
For both data sets, all data points are excluded if that raven had less
than 5 GPS points and the movement decisions was the negative for that
binomial model (didn’t leaves its territory or didn’t visit the hunting
area).
## dataset for part 1 of conditional model
ws_model_data <- read_csv(here("data", "clean", "commute_data.csv")) %>%
#restricting to only winter study months
filter((paste(month, day, sep = "-") >= "11-15" &
paste(month, day, sep = "-") <= "12-15") |
(paste(month, day, sep = "-") >= "3-1" &
paste(month, day, sep = "-") <= "3-30")) %>%
#removing days when there is less than 5 GPS point
#unless the result is Jardine
filter(!(n_point < 5 & terr_bin == F)) %>%
#only columns used in model
dplyr::select(terr_bin, raven_id, rf_active_kill, bms_window_1, hunt_season, take_high_low, rf_avg_terr_kill_density, dist2nentrance,
study_period, temp_max, snow_depth, prop_group_left_terr) %>%
#making sure rows are complete
filter(complete.cases(.))
## dataset for part 2 of conditional model
hunt_model_data <- read_csv(here("data", "clean", "commute_data.csv")) %>%
#only have days ravens decided to leave territory
filter(terr_bin == 1) %>%
#removing days when there is less than 5 GPS point
#unless the result is Jardine
filter(!(n_point < 5 & hunt_bin == F)) %>%
#only columns used in model
dplyr::select(hunt_bin, raven_id, bms_window_1, hunt_season, take_high_low, dist2nentrance, study_period, temp_max, snow_depth, prop_group_visit_hunt) %>%
#making sure rows are complete
filter(complete.cases(.)) Part 1 of conditional model
The first part of the conditional model predicts if a raven will
leaves it territory or not.
DEPENDENT VARIABLE
terr_bin
1 = left territory
0 = stayed on territory
I ended up trying a three different covariates to represent the
hunting element of the model because I don’t know how ravens view the
resource or the thresholds for availability that they consider viable.
For examples, 10 and 15 kills are probably basically the same thing. Its
a lot of potential food. But where is that line drawn. Is 1 and 5
different enough? What about 5 and 10? Or maybe 1 is all it takes. Or
just hunters trying. It also allows for a little flexibility without the
most precise daily data for hunting.
1. bms_window: The most specific is the a measure of the available
biomass.
mod_terr_bms1 <- glmer(terr_bin ~ (1|raven_id) + rf_active_kill * scale(bms_window_1) + scale(rf_avg_terr_kill_density) +
scale(dist2nentrance) + study_period * scale(temp_max) + scale(snow_depth) + scale(prop_group_left_terr),
data = ws_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_terr_bms1)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula: terr_bin ~ (1 | raven_id) + rf_active_kill * scale(bms_window_1) +
## scale(rf_avg_terr_kill_density) + scale(dist2nentrance) +
## study_period * scale(temp_max) + scale(snow_depth) + scale(prop_group_left_terr)
## Data: ws_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 1137.4 1203.3 -556.7 1113.4 1790
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.1126 0.1386 0.2226 0.3763 3.7325
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 2.028 1.424
## Number of obs: 1802, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.88131 0.38452 7.493 6.71e-14 ***
## rf_active_killTRUE -0.99078 0.37465 -2.645 0.00818 **
## scale(bms_window_1) -0.09206 0.13096 -0.703 0.48205
## scale(rf_avg_terr_kill_density) 0.40063 0.38877 1.031 0.30277
## scale(dist2nentrance) -0.29363 0.36689 -0.800 0.42352
## study_periodlate -0.57310 0.20294 -2.824 0.00474 **
## scale(temp_max) -0.18321 0.11411 -1.606 0.10838
## scale(snow_depth) 0.23833 0.13882 1.717 0.08601 .
## scale(prop_group_left_terr) -0.06791 0.09664 -0.703 0.48222
## rf_active_killTRUE:scale(bms_window_1) 0.29844 0.29799 1.001 0.31659
## study_periodlate:scale(temp_max) 0.05543 0.16587 0.334 0.73824
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) rf__TRUE s(__1) s(____ scl(2) stdy_p scl(t_) scl(s_) s(___)
## rf_ctv_TRUE 0.005
## scl(bms__1) -0.058 -0.054
## scl(rf____) 0.187 -0.009 0.023
## scl(dst2nn) 0.077 0.022 0.052 0.083
## study_prdlt -0.300 -0.121 0.121 0.003 -0.001
## scl(tmp_mx) 0.016 -0.013 -0.165 -0.014 -0.002 -0.075
## scl(snw_dp) 0.149 0.087 -0.613 0.001 -0.003 -0.512 0.225
## scl(prp___) -0.040 0.017 -0.077 0.008 -0.039 0.153 0.070 -0.113
## r__TRUE:(__ -0.005 -0.108 -0.228 -0.020 -0.014 0.061 0.009 -0.045 0.006
## stdy_pr:(_) 0.018 0.062 0.139 0.011 0.004 -0.142 -0.650 -0.008 0.033
## r__TRUE:
## rf_ctv_TRUE
## scl(bms__1)
## scl(rf____)
## scl(dst2nn)
## study_prdlt
## scl(tmp_mx)
## scl(snw_dp)
## scl(prp___)
## r__TRUE:(__
## stdy_pr:(_) -0.052- hunt_season: The least specific is just whether it is within the hunting season
mod_terr_hseason <- glmer(terr_bin ~ (1|raven_id) + rf_active_kill * hunt_season + scale(rf_avg_terr_kill_density) +
scale(dist2nentrance) + study_period * scale(temp_max) + scale(snow_depth) + scale(prop_group_left_terr),
data = ws_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_terr_hseason)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula:
## terr_bin ~ (1 | raven_id) + rf_active_kill * hunt_season + scale(rf_avg_terr_kill_density) +
## scale(dist2nentrance) + study_period * scale(temp_max) +
## scale(snow_depth) + scale(prop_group_left_terr)
## Data: ws_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 1138.1 1204.0 -557.0 1114.1 1790
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.1242 0.1391 0.2237 0.3719 3.2319
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 1.979 1.407
## Number of obs: 1802, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.81486 0.44744 6.291 3.15e-10 ***
## rf_active_killTRUE -1.89385 1.46694 -1.291 0.19670
## hunt_seasonTRUE 0.08573 0.31852 0.269 0.78780
## scale(rf_avg_terr_kill_density) 0.41317 0.38467 1.074 0.28278
## scale(dist2nentrance) -0.28234 0.36275 -0.778 0.43637
## study_periodlate -0.60506 0.21857 -2.768 0.00564 **
## scale(temp_max) -0.20334 0.11783 -1.726 0.08440 .
## scale(snow_depth) 0.20603 0.10679 1.929 0.05369 .
## scale(prop_group_left_terr) -0.06719 0.09664 -0.695 0.48691
## rf_active_killTRUE:hunt_seasonTRUE 0.99883 1.50517 0.664 0.50694
## study_periodlate:scale(temp_max) 0.08609 0.16754 0.514 0.60737
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) rf__TRUE h_TRUE s(____ scl(2) stdy_p scl(t_) scl(s_) s(___)
## rf_ctv_TRUE -0.098
## hnt_ssnTRUE -0.527 0.161
## scl(rf____) 0.162 -0.007 -0.006
## scl(dst2nn) 0.068 0.014 -0.002 0.084
## study_prdlt -0.020 -0.038 -0.403 0.004 -0.005
## scl(tmp_mx) 0.159 -0.040 -0.292 -0.009 0.007 0.072
## scl(snw_dp) 0.073 0.053 0.095 0.012 0.034 -0.535 0.125
## scl(prp___) -0.020 -0.085 -0.030 0.010 -0.037 0.161 0.062 -0.216
## r__TRUE:_TR 0.102 -0.969 -0.168 0.005 -0.007 0.017 0.034 -0.051 0.089
## stdy_pr:(_) -0.091 0.029 0.212 0.006 -0.004 -0.226 -0.666 0.107 0.037
## r__TRUE:
## rf_ctv_TRUE
## hnt_ssnTRUE
## scl(rf____)
## scl(dst2nn)
## study_prdlt
## scl(tmp_mx)
## scl(snw_dp)
## scl(prp___)
## r__TRUE:_TR
## stdy_pr:(_) -0.013- take_high_low: in between the other 2, its a categorical variable with either high, low, or zero biomass availability.
mod_terr_hl <- glmer(terr_bin ~ (1|raven_id) + rf_active_kill * take_high_low + scale(rf_avg_terr_kill_density) +
scale(dist2nentrance) + study_period * scale(temp_max) + scale(snow_depth) + scale(prop_group_left_terr),
data = ws_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_terr_hl)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula: terr_bin ~ (1 | raven_id) + rf_active_kill * take_high_low +
## scale(rf_avg_terr_kill_density) + scale(dist2nentrance) +
## study_period * scale(temp_max) + scale(snow_depth) + scale(prop_group_left_terr)
## Data: ws_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 1138.5 1215.5 -555.3 1110.5 1788
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.1986 0.1375 0.2231 0.3686 2.6212
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 2.022 1.422
## Number of obs: 1802, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.60739 0.44241 5.894 3.78e-09 ***
## rf_active_killTRUE -1.22097 0.46979 -2.599 0.00935 **
## take_high_lowlow 0.36468 0.26155 1.394 0.16323
## take_high_lowzero 0.26100 0.39265 0.665 0.50624
## scale(rf_avg_terr_kill_density) 0.42870 0.38864 1.103 0.26999
## scale(dist2nentrance) -0.26472 0.36674 -0.722 0.47041
## study_periodlate -0.44324 0.25097 -1.766 0.07738 .
## scale(temp_max) -0.18723 0.11802 -1.586 0.11264
## scale(snow_depth) 0.30538 0.12153 2.513 0.01198 *
## scale(prop_group_left_terr) -0.05587 0.09727 -0.574 0.56573
## rf_active_killTRUE:take_high_lowlow 0.79716 0.76653 1.040 0.29836
## rf_active_killTRUE:take_high_lowzero -0.67626 1.52699 -0.443 0.65786
## study_periodlate:scale(temp_max) 0.08134 0.17060 0.477 0.63353
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1All 3 models are pretty competitive.
AIC(mod_terr_bms1) #equally good## [1] 1137.357AIC(mod_terr_hseason) #equally good## [1] 1138.087AIC(mod_terr_hl)## [1] 1138.526It actually didn’t matter which hunting covariate I used because they
were all not significant. Instead, as expected, in most of the models
the presence of an active kill within 1 km of a ravens territory lead to
less chance of the raven leaving its territory. The interaction term in
all 3 models was not significant, meaning that the presence of an active
kill did not change the impact hunter gutpile availability had on raven
movement.
The binary hunting season covariate in the second model did lead to a
change in the significance of the active kill covariate. This is because
the added interaction term (with active wolf kill) had a high standard
error, even though the effect size and direction were basically the
same.
The average kill density in a ravens territory did not impact movement
decisions. So they don’t consider the past or prior knowledge of their
territory and are only responding to more immediate stimuli. This makes
sense when considering that a high productivity territory is still
unlikely to have a kill made each day. Then their response to no
immediate kills in their territory is to leave, which is still a gamble
since you don’t know what the food situation will be like in Gardiner or
elsewhere; however, in most cases those human sites will still be less
of a gamble than a raven in a high productivity territory.
The study period being early or late winter has a negative effect in the
late winter in all 3 of the models (even though it isn’t significant in
model 3), which follows my prediction about how pre-breeding behaviors
would impact raven movement by keeping them on territory more
often.
The maximum daily temperature had a negative effect in all three models,
although it was borderline in 2 of the models. Higher temperatures
lowered the chance of a raven leaving its territory. A good reason for
this might be that the colder days require more energy to maintain body
temperature, so a more guaranteed food sources is taken. Then on warmer
days when temperature regulation is easier, they don’t risk as much by
staying on their territory. An interaction between temperature and study
period was tested to tell if ravens were influenced by temperature
differently at different times of year and the effect was insignificant
and is not included here.
Snow depth had the same effect found from the Walker et al. study that
greater snow depth increased the chances of the raven being in
anthropogenic hunting areas (leaving their territory). This isn’t a
perfect conclusion though because even though they leave their
territory, they could still be staying in the national park. However, it
does agree with the alternative logic that higher snow depth leads to
ungulate migration and more potential hunting availability. So this
might be a cue that they are not following or attempting to gain
knowledge about actual hunting availability (hence a lack of effect for
the actual hunting covariate) and are instead following proxies for it.
snow depth and the hunting biomass coavriates have a high correlation in
the model output. This is likely because the biomass calculation takes
into account elk migration timing, which is heavily influenced by snow
depth.
One super interesting thing to note is that I ran this model with the
group travel covariate before adding the temperature, and the group
travel stopped being significant after the addition of the temperature.
So it would seem like they don’t take into account the other ravens that
much and instead are all responding to the same stimuli.
Here is the bootstrapped parameter confidence intervals for model 1
using the biomass estimate as the hunting covariate.
Part 2 of conditional model
The second part of the conditional model predicts if, when a raven
left its territory, if it visited the Gardiner hunting region.
DEPENDENT VARIABLE
hunt_bin
1 = visited hunting
0 = visited other place
Again, I compared models using the same three hunting covariates.
However, this time I removed the wolf kill and study period
covariates.
I don’t consider wolf kills anymore because, at this point in the model,
the raven has already left its territory. It is true that a raven could
travel to a wolf kill outside of its territory, but I am interested in
the decision to travel to the Gardiner hunting region, so those other
options don’t matter as much. That includes other cities and towns. This
part of the conditional model acknowledges their presence, but isn’t
really interested in them specifically.
I don’t consider study period anymore because, again, in this part of
the conditional model the raven has already decided to leave its
territory. The breeding behavior hypothesis was that ravens would want
to stay on their territory more during late winter to
perform breeding behaviors. This doesn’t matter anymore here.
1. bms_window: The most specific is the a measure of the available
biomass.
mod_hunt_bms1 <- glmer(hunt_bin ~ (1|raven_id) + scale(bms_window_1) + scale(dist2nentrance) +
scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth),
data = hunt_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_hunt_bms1)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula:
## hunt_bin ~ (1 | raven_id) + scale(bms_window_1) + scale(dist2nentrance) +
## scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth)
## Data: hunt_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 3481.0 3524.9 -1733.5 3467.0 3904
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.5605 -0.1822 0.2984 0.5594 3.1345
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 3.834 1.958
## Number of obs: 3911, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.46902 0.46927 0.999 0.31757
## scale(bms_window_1) 0.60513 0.10813 5.597 2.19e-08 ***
## scale(dist2nentrance) -2.15348 0.50516 -4.263 2.02e-05 ***
## scale(prop_group_visit_hunt) 0.50689 0.05041 10.055 < 2e-16 ***
## scale(temp_max) -0.27843 0.04717 -5.902 3.58e-09 ***
## scale(snow_depth) -0.13865 0.05102 -2.718 0.00658 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) s(__1) scl(2) s(___) scl(t_)
## scl(bms__1) 0.015
## scl(dst2nn) 0.059 -0.068
## scl(prp___) 0.007 -0.315 -0.016
## scl(tmp_mx) -0.014 -0.200 0.018 0.143
## scl(snw_dp) -0.013 -0.045 -0.012 0.036 0.396- hunt_season: The least specific is just whether it is within the hunting season
mod_hunt_hseason <- glmer(hunt_bin ~ (1|raven_id) + hunt_season + scale(dist2nentrance) +
scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth),
data = hunt_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_hunt_hseason)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula: hunt_bin ~ (1 | raven_id) + hunt_season + scale(dist2nentrance) +
## scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth)
## Data: hunt_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 3463.7 3507.6 -1724.9 3449.7 3904
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.7099 -0.1474 0.2925 0.5361 2.9754
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 3.548 1.884
## Number of obs: 3911, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.085022 0.453716 0.187 0.851
## hunt_seasonTRUE 0.804120 0.102174 7.870 3.54e-15 ***
## scale(dist2nentrance) -2.128294 0.485719 -4.382 1.18e-05 ***
## scale(prop_group_visit_hunt) 0.470581 0.051169 9.197 < 2e-16 ***
## scale(temp_max) -0.315563 0.048724 -6.477 9.38e-11 ***
## scale(snow_depth) -0.006388 0.051114 -0.125 0.901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) h_TRUE scl(2) s(___) scl(t_)
## hnt_ssnTRUE -0.093
## scl(dst2nn) 0.067 -0.021
## scl(prp___) 0.044 -0.354 -0.025
## scl(tmp_mx) 0.015 -0.274 0.017 0.165
## scl(snw_dp) -0.027 0.175 -0.006 -0.063 0.322- take_high_low: in between the other 2, its a categorical variable with either high, low, or zero biomass availability.
mod_hunt_hl <- glmer(hunt_bin ~ (1|raven_id) + take_high_low + scale(dist2nentrance) +
scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth),
data = hunt_model_data,
family = "binomial",
nAGQ = 40,
control = cntrl)
summary(mod_hunt_hl)## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 40) [glmerMod]
## Family: binomial ( logit )
## Formula: hunt_bin ~ (1 | raven_id) + take_high_low + scale(dist2nentrance) +
## scale(prop_group_visit_hunt) + scale(temp_max) + scale(snow_depth)
## Data: hunt_model_data
## Control: cntrl
##
## AIC BIC logLik -2*log(L) df.resid
## 3462.7 3512.9 -1723.3 3446.7 3903
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.9852 -0.1466 0.2924 0.5393 2.9563
##
## Random effects:
## Groups Name Variance Std.Dev.
## raven_id (Intercept) 3.579 1.892
## Number of obs: 3911, groups: raven_id, 20
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.09745 0.46733 2.348 0.0189 *
## take_high_lowlow -0.38472 0.16680 -2.306 0.0211 *
## take_high_lowzero -1.00728 0.14107 -7.140 9.31e-13 ***
## scale(dist2nentrance) -2.14450 0.48788 -4.396 1.10e-05 ***
## scale(prop_group_visit_hunt) 0.46171 0.05127 9.006 < 2e-16 ***
## scale(temp_max) -0.33422 0.04959 -6.740 1.58e-11 ***
## scale(snow_depth) -0.06928 0.05765 -1.202 0.2294
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tk_hgh_lwl tk_hgh_lwz scl(2) s(___) scl(t_)
## tk_hgh_lwlw -0.203
## tk_hgh_lwzr -0.233 0.688
## scl(dst2nn) 0.057 0.018 0.028
## scl(prp___) -0.052 0.084 0.313 -0.023
## scl(tmp_mx) -0.082 0.193 0.318 0.019 0.177
## scl(snw_dp) -0.079 0.454 0.187 0.002 -0.017 0.373Of the 3 models, the hunting season and high/low hunting predictors are equal.
AIC(mod_hunt_bms1)## [1] 3480.992AIC(mod_hunt_hseason) #equally good## [1] 3463.712AIC(mod_hunt_hl) #equally good## [1] 3462.684In all of the models the hunting covariate was significant and
followed the trend of more hunting, more likely the raven is to visit
the hunting area.
The distance to the hunting area was also always significant with ravens
holding territories closer to the hunting area visiting more frequently.
Makes sense that the less time and energy it takes to get there makes it
more worth checking out the area. For some ravens that are really close,
it also gives them the advantage of potentially being able to hear
gunshots that indicate potential hunter success.
The proportion of other ravens that are visiting the hunting area has a
positive effect. When considered in conjunction with the effect of the
group covariate in part 1 of the conditional model: ravens aren’t
influenced by other ravens when deciding to leave their territory;
however, if they do choose to leave they are often visiting the same
destinations as the rest of the ravens that leave their territories. So
if they choose to leave, which is a decision based on abiotic factors
like weather and available local food, they are utilizing social cues
and shared information.
The maximum daily temperature had a negative effect in all three models,
lowering the chance of a raven visiting the hunting area if it decided
to leave its territory during warmer weather.
The effect of snow depth is uncertain from these models. Only model 1
found a significant effect and the other two models were not significant
with different effect directions (although both almost 0).
Here is the bootstrapped parameter confidence intervals for model 1
using the biomass estimate as the hunting covariate.
Figures
Here is a table that shows the number of times raven made each decision. Beth had the idea to make some kind of heat map similar to the map below that has individual examples of ravens GPS points, but for raven decisions. This would be so there was some, more easily understandable (the giant mass of GPS points is hard to comprehend and compare), visual example. The Gardiner hunting region and the territory would be heat map areas and then the times that the raven left its territory but didn’t go to Gardiner would leave the GPS points like map 1.B. This would mean that you could only have 1 raven per map so that the heat map reflected that individuals decisions.
(raven_decisions <- read_csv(here("data", "clean", "commute_data.csv")) %>%
group_by(raven_id) %>%
summarize(terr = sum(terr_bin == FALSE),
other = sum(terr_bin == TRUE & hunt_bin == FALSE),
hunt = sum(hunt_bin == TRUE)) %>%
# adding column for total sample size for each raven
mutate(n = hunt + other + terr))## # A tibble: 20 × 5
## raven_id terr other hunt n
## <chr> <int> <int> <int> <int>
## 1 7484 62 8 64 134
## 2 7485 108 220 0 328
## 3 7489 51 155 275 481
## 4 7489_2 23 14 24 61
## 5 7490_3 89 84 239 412
## 6 7492 92 144 325 561
## 7 7493_2 63 48 1 112
## 8 7494 407 184 0 591
## 9 7495 17 19 115 151
## 10 7530 238 50 441 729
## 11 7531 65 81 116 262
## 12 7561 99 194 189 482
## 13 7565 85 111 9 205
## 14 7595 38 160 149 347
## 15 7640_3 95 69 289 453
## 16 7652_2 38 47 140 225
## 17 7665 49 156 247 452
## 18 7672 114 36 98 248
## 19 8900 10 37 77 124
## 20 8902 5 3 1 9But I think an even better option would be a bar chart with 3 levels
showing the proportion of days making whatever decisions (similar to how
we handled the raven foraging).
Here is an visual example of three different ravens with
territories at different distances from the Gardiner hunting region area
and their GPS points.
Of the three ravens, the orange raven with its territory at Old Faithful
is the only one that doesn’t visit the hunting area which is why it
looks the same in both maps. Instead, its trips are consistently to the
closer town of West Yellowstone, presumably to feed on human refuse. It
probably makes this decision because the time investment to travel up to
the Gardiner hunting region is not worth it when an alternative location
with consistent foraging is nearby. Even though purple is a similar
distance to West Yellowstone where orange visits frequently, it chooses
to travel to the north instead. It probably makes this choice because
unlike orange, the time investment is about the same between the two
locations. And Gardiner has a much higher level of hunting offering a
potentially better foraging opportunity while also have human refuse as
a back up. Almost all trips north for purple resulted in a visit to the
Gardiner hunting region, and the few remaining points up north are
probably because of a missed fix in the hunting area.Most of the time
when the purple chooses to leave its territory, but not visit the
Gardiner hunting region, it is actually still hanging out around its
territory but just outside of the 1 kilometer around the 90% minimum
convex polygon I am currently considering their territory. Green is so
close to the Gardiner hunting region that it only makes sense that it
visits so often, given that the flight time for that trip is less than
30 minutes. On days that it leaves its territory but does not visit the
Gardiner hunting region it visits various areas in the northern range
inside the park and even ventures eastward a few times during October
before it gets too cold. One super interesting thing to note is that you
would think that there would be more obvious instances of ravens
visiting wolf kills outside their territories which would show up as
small concentrations of GPS points in map B. However, this almost never
occurs, or at least isn’t obvious. I think this is because either the
carcass is close enough to their territory that I still consider the
raven as having not left. Or, ravens will frequently visit wolf kills
outside their territory, followed by a trip to the Gardiner hunting
area. This second explanation actually lines up with some of my
experiences seeing a group of ravens fly into a carcass sometime in the
morning, only to leave not long after. I look into this a farther down
using some tables.
Map A shows the all GPS points made by each of the three ravens. Map B
shows the GPS points for the three ravens when they choose to exit their
territories (highlighted in red), but did not visit the Gardiner hunting
region.
Here is a heat map of the
raven GPS points outside the park from November and March along with a
polygon denoting the area used to determine if a raven attempted to
search for hunter created resources during the MTFWP rifle hunting
season and the tribal bison hunt (hereafter Gardiner hunting region).
The Gardiner hunting region is defined as the space 5 km from all roads
within 10 km north of the national park boundary. This space has a high
density of hunting activity in close proximity to the northern range of
the park. The 5 km buffer around roads was used as a reasonable distance
for a hunter to travel. There is certainly successful hunting attempts
in the areas outside this polygon, but the relative number of those will
be low compared to hunting within the polygon.
This polygon does include the town of Gardiner along with the local
landfill and water treatment ponds that ravens have been documented
using as locations to forage since I made the assumption that a raven
visiting this area would always attempt to find hunter offal, even if
unsuccessful. Only 26% of trips to the Gardiner hunting region during
the hunting season resulted in a trip to the landfill and water
treatment pond.
Here is a map of the relevant
polygons used including the study area of Yellowstone National Park, the
northern range of Yellowstone, and raven territories calculated using
90% minimum convex polygons of their breeding season GPS data. All raven
used for this study have territories within the boundary of the national
park. In 2 cases where a territorial pair had both individuals GPS
tagged, only the female was used since the GPS fix rate was higher due
to better battery levels resulting from less coverage of the solar panel
during the winter.
## Wolf kill visits I looked at how often
ravens were visiting wolf kills when they left their territory because
it looked like they didn’t visit kills that often when they left their
territory but didn’t visit the Gardiner hunting region (map 1.B).
source(here("scripts", "exploratory", "wolf_kill_visits.R"))## Warning: One or more parsing issues, call `problems()` on your data frame for details,
## e.g.:
## dat <- vroom(...)
## problems(dat)#table for days visiting wolf kills with no hunting visit
leave_no_hunt_wolf_kills## # A tibble: 10 × 4
## raven_id days_visit total_days prop_visit
## <chr> <int> <int> <dbl>
## 1 7490_3 6 27 0.222
## 2 7492 3 63 0.0476
## 3 7531 7 39 0.179
## 4 7561 21 133 0.158
## 5 7595 13 126 0.103
## 6 7640_3 6 36 0.167
## 7 7652_2 1 21 0.0476
## 8 7665 9 98 0.0918
## 9 8900 1 12 0.0833
## 10 8902 1 3 0.333# table for days visiting wolf kills with hunting visit
hunt_wolf_kills## # A tibble: 16 × 4
## raven_id days_visit total_days prop_visit
## <chr> <int> <int> <dbl>
## 1 7484 11 63 0.175
## 2 7489 16 257 0.0623
## 3 7490_3 11 152 0.0724
## 4 7492 17 248 0.0685
## 5 7495 4 108 0.0370
## 6 7530 20 378 0.0529
## 7 7531 15 100 0.15
## 8 7561 9 142 0.0634
## 9 7565 3 6 0.5
## 10 7595 7 132 0.0530
## 11 7640_3 6 176 0.0341
## 12 7652_2 10 84 0.119
## 13 7665 11 207 0.0531
## 14 7672 7 68 0.103
## 15 8900 8 33 0.242
## 16 8902 1 1 1It looks like wolf kill visits are not a large portion of trips outside of the territory, regardless of if the raven ends up in the Gardiner hunting region or not. This tracks with the foraging paper and the relative importance of natural carrion to anthropogenic resources used by most ravens. It is worth noting that a fair number of times ravens do visit wolf kills before preceding to search for hunter gutpiles.